In this paper we are interested in lifting a prescribed group of automorphisms of a finite graph via regular covering projections. Let
Γ
\Gamma
be a finite graph and let
A
u
t
(
Γ
)
\mathrm {Aut}(\Gamma )
be the automorphism group of
Γ
\Gamma
. It is well known that we can always find a finite graph
Γ
~
\tilde {\Gamma }
and a regular covering projection
℘
:
Γ
~
→
Γ
\wp \colon \tilde {\Gamma } \to \Gamma
such that
A
u
t
(
Γ
)
\mathrm {Aut}(\Gamma )
lifts along
℘
\wp
. However, for constructing peculiar examples and in applications it is often important, given a subgroup
G
G
of
A
u
t
(
Γ
)
\mathrm {Aut}(\Gamma )
, to find
℘
\wp
along which
G
G
lifts but no further automorphism of
Γ
\Gamma
does, or even that
A
u
t
(
Γ
~
)
\mathrm {Aut}(\tilde {\Gamma })
is the lift of
G
G
. In this paper, we address these problems.